Given the asymptotes and eccentricity write the equation of the hyperbola

The video tutorial explains how to determine the center of a hyperbola given its asymptotes. It discusses the role of eccentricity in identifying the values of a, b, and c, and verifies these values using the equation a^2 + b^2 = c^2. The tutorial concludes by deriving the hyperbola's equation, emphasizing the choice between horizontal and vertical orientations based on the asymptote's form.

What is the given asymptote equation in the video?

• y = ± 5/3

• y = ± 4/3

• y = ± 3/5

• y = ± 3/4

How is the center of the hyperbola determined in the video?

• By ensuring the center is at (0,0)

• By calculating the eccentricity

• By verifying the asymptote equation

• By checking if the asymptote is vertical

What is the formula for eccentricity as discussed in the video?

• a/c

• c/a

• b/a

• a/b

Which values are identified for a, b, and c in the video?

• a = 3, b = 4, c = 5

• a = 4, b = 3, c = 5

• a = 3, b = 5, c = 4

• a = 5, b = 3, c = 4

What is the final equation of the hyperbola derived in the video?

• Y^2/16 - X^2/9 = 1

• X^2/16 + Y^2/9 = 1

• X^2/9 - Y^2/16 = 1

• X^2/16 - Y^2/9 = 1